R D Sharma Solutions for Chapter: Derivative as a Rate Measurer, Exercise 1: VERY SHORT ANSWER QUESTIONS (VSAQs)

A cone whose height is always equal to its diameter is increasing in volume at the rate of $40 {\mathrm{cm}}^3/\sec$. At what rate is the radius increasing when its circular base area is $1 {\mathrm{m}}^2$?

A cylindrical vessel of radius $0.5 \mathrm{m}$ is filled with oil at the rate of $0.25\pi {\mathrm{m}}^3/\mathrm{minute}$ The rate at which the surface of the oil is rising, is

The distance moved by the particle in time t is given by $x=t^3-12t^2+6t+8$. At the instant when its acceleration is zero, the velocity is

The altitude of a cone is $20 \mathrm{cm}$ and its semi-vertical angle is $30°$. If the semi-vertical angle is increasing at the rate of $2°$ per second, then the radius of the base is increasing at the rate of

For what values of $x$ is the rate of increase of $x^3-5x^2+5x+8$ is twice the rate of increase of $x$?

The coordinates of the point on the ellipse $16x^2+9y^2=400$ where the ordinate decreases at the same rate at which the abscissa increases, are

The radius of the base of a cone is increasing at the rate of $3 \mathrm{cm}/\mathrm{minute}$ and the altitude is decreasing at the rate of $4 \mathrm{cm}/\mathrm{minute}$. The rate of change of lateral surface when the radius $=7 \mathrm{cm}$ and altitude $24 \mathrm{cm}$ 

The radius of a sphere is increasing at the rate of $0.2 \mathrm{cm}/\sec$. The rate at which the volume of the sphere increase when radius is $15 \mathrm{cm}$, is